Block #269,950

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 2:15:08 PM · Difficulty 9.9520 · 6,521,702 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

c82ce8608cadfcf661217959a7e5cdd57f1442756228148b55c946900879ea8c

View on Chainz ↗

Height

#269,950

Difficulty

9.952007

Transactions

Size

7.67 KB

Version

Bits

09f3b6b8

Nonce

141,271

Timestamp

11/23/2013, 2:15:08 PM

Confirmations

6,521,702

Merkle Root

49e4958fa79e2a0178c4d81114a9f4b5777e96d5cf30cdda828f4e1773557f15

Transactions (4)

Coinbaseb2e7b0842742e2…d961cce21a0d2a

1 in → 50 out10.0600 XPM1.72 KB

ANQKf2g4…29NaVj23 AabHNb1B…GRoingRy ARpndEmc…Hg792kEk ANHbaxZp…XjnHCJJs AVzhvfTX…ZzNJYq61

ab51c58f7ead5c…0db229457f8784

1 in → 2 out5.0788 XPM226 B

ANbR8r54…1tQsEvQ6 AcNkWsAZ…wVEvsiKj

5c2a53f8ec41eb…8cd392ea7130c4

33 in → 2 out4.0100 XPM4.84 KB

AXKUscLN…z2VJBYvk AP2xfJw3…BGdWi2vZ

0c582bdf516b3a…12cec1ba520e2f

5 in → 2 out1.0248 XPM820 B

AQQEZrze…wgfK19Fz AQ6XdKUd…zgnbq1Tb

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.671 × 10⁹¹(92-digit number)

16716122405720250303…62334088236187474079

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.671 × 10⁹¹(92-digit number)

16716122405720250303…62334088236187474079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.671 × 10⁹¹(92-digit number)

16716122405720250303…62334088236187474081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

3.343 × 10⁹¹(92-digit number)

33432244811440500606…24668176472374948159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.343 × 10⁹¹(92-digit number)

33432244811440500606…24668176472374948161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

6.686 × 10⁹¹(92-digit number)

66864489622881001212…49336352944749896319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.686 × 10⁹¹(92-digit number)

66864489622881001212…49336352944749896321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.337 × 10⁹²(93-digit number)

13372897924576200242…98672705889499792639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.337 × 10⁹²(93-digit number)

13372897924576200242…98672705889499792641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.674 × 10⁹²(93-digit number)

26745795849152400485…97345411778999585279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.674 × 10⁹²(93-digit number)

26745795849152400485…97345411778999585281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer